Standardized actuators are limited to repeating a predefined set of tasks. Therefore, this paper proposes a non-standardized end-effector (NSEE) integrated with depth imaging capabilities, which exhibits enhanced adaptability and optimization capacities for specialized applications such as personalized precision manufacturing, assembly, packaging. NSEE positioning algorithm was also proposed by constructing a vector-product. 3D coordinates could be obtained under the circumstances of the coexistence of radial distortion with tangential distortion by using pinhole-explicit implicit method on a simple Kinect depth image. The range of the actual rotation angles of the joints was determined by applying the inverse kinematics model and vector-product. Arm pitch angle was iterated to solve all the efficient solutions by inverse kinematics. All solutions were checked with forward kinematics. The optimal solution was calculated in accordance with the principle of the highest operational efficiency. The simulation results show that the algorithm could be used for NSEE positioning, and the accuracy is in the scale of millimeters. The positioning efficiency was improved by approximately 10%, and the accuracy has been raised by about 1%. The positioning algorithm can meet accurate positioning requirements.